University tuition fees are "preposterously" low and must rise if British higher education is to remain world class, the chancellor of Oxford university said today.

Lord Patten, who was a Tory cabinet minister in the 1980s, said universities should be allowed to charge the fees they wanted, as long as they admitted students on intellectual merit and not their ability to pay.

The amount universities receive from tuition fees and government grants barely covers half the £16,000 it costs to teach an undergraduate at Oxford, Patten told the annual conference of the Independent Schools Council in London. The university had to make up the rest in endowments and alumni donations.

Tuition fees – currently £3,225 per year in English universities – are less than half the sum lecturers pay annually for their children's childcare, Patten, a former governor of Hong Kong, said.

"It is preposterous that we can only charge for teaching an undergraduate less than half the cost that those who do that teaching would have to pay for creche facilities for their own children," he said.

Universities should not stop receiving public funds for teaching because it is a "common good which deserves to have public assistance," he said. "But I would be prepared to cap the funding of our teaching grant if we were able as a result to set whatever tuition fee we wanted. Oxford gets about half [the cost of teaching an undergraduate in a year] in teaching grants and tuition fees. I don't think it is realistic to say that the gap should be closed by the taxpayer; we have to use our endowments and alumni. But it is plain that we are going to require higher tuition fees."

Patten's comments come ahead of an independent review on fees, led by the former BP chief executive, Lord Browne. The review is due after the general election. On Thursday, the Government's Higher Education Funding Council for England will announce budgets for individual universities.

Patten attacked the government for "insulting" universities with plans for nearly £1bn of cuts.

Last month, universities were asked to save £449m in 2010-11. On top of this, Alistair Darling, the chancellor, announced higher education savings of £600m in the pre-budget report in December. The elite Russell Group of universities, which includes Oxford and Cambridge, warned that the cuts could bring universities "to their knees" within six months.

Patten said: "Whereas governments in France, Germany and the US have recently announced big increases in university spending, in this country higher education faces £1bn of cuts with more in the pipeline. With cuts on this scale, it is worse than insulting for Lord Mandelson – the business secretary in charge of universities – to tell us that the science budget is being protected and for the higher education minister to advise universities to apply to America for research funding."

Universities in the UK "purport" to do the same thing, he said. Instead, they should specialise in particular subjects.

"We pretend to give every 18-year-old qualified to go on to higher education the same experience at the same sort of institution," he said. "That represents an expensive and inefficient delusion. We should differentiate between different sorts of institution, prize these distinctions and devote our energy to ensuring reasonable movement by students from one sort of institution to another, according to ability. It is nonsense to think that every university should have a physics and a philosophy department. We should be much more specialised."

Patten hinted that sometimes private school headteachers and their pupils claimed "class bias" when they failed to get into Oxford or Cambridge. "I believe we do our best to run a system that chooses the most qualified and suitable, from the ranks of many who appear to be qualified," he said. But he said he would also strongly resist "the suggestion that at a university like Oxford, we should abandon a meritocratic test imaginatively applied in favour of social engineering."

Meanwhile, David Willetts, the Tory universities secretary, said more than twice as many students will be left without a place at university this year compared to last.

The Conservatives have analysed last year's applications and found that 275,000 students are likely to be without a place this summer, compared to 135,000 last year.

Speaking before a House of Commons, Willetts said: "The Government's failure to tackle the places crisis means more than a quarter of a million people could miss out on the education they deserve. Yet again, young people are proving to be the biggest victims of Labour's recession." There will be at least 6,000 fewer places this year than last year, despite record numbers of students shunning the job market and applying for university.